Spectroscopic characterization of photoresponsive systems: from chromoproteins to switchable and caged compounds

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Spectroscopic Characterization of

Photoresponsive Systems: from Chromoproteins to Switchable and Caged Compounds

Dissertation

zur Erlangung des Doktorgrades der Naturwissenschaften

vorgelegt beim Fachbereich 14 der Goethe-Universität Frankfurt am Main

von

Christopher-Andrew Hammer aus Caracas (Venezuela)

Frankfurt am Main 2018 (D30)

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Vom Fachbereich 14 der

Goethe-Universität Frankfurt am Main als Dissertation angenommen.

Dekan Prof. Dr. Clemens Glaubitz 1. Gutachter Prof. Dr. Josef Wachtveitl 2. Gutachter Prof. Dr. Alexander Heckel

Datum der Disputation:

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Working hard is important.

But there is something that matters even more, believing in yourself.

Harry Potter and the Order of the Phoenix - J. K. Rowling

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List of Figures

2.1 Energy diagram of one-photon and two-photon absorption . . . 8

2.2 Schematic representation of the main difference between 1PA and 2PA . 8 2.3 The four essential states for 2PA . . . 11

2.4 The introduction of extendedπ-systems within a molecule enhances the σ_2P . . . 12

2.5 Schematic z-scan setup for the determination ofσ2P . . . 13

3.1 Fluorescence-related publications in different research fields . . . 19

3.2 Jabłoński diagram with schematic representation of processes occurring between the states . . . 20

3.3 Schematic representation of optical gating . . . 23

3.4 Schematic representation of the Kerr shutter principle . . . 26

4.1 Uncaging reaction mechanisms . . . 30

4.2 Numbering and chemical structure of coumrin . . . 31

4.3 Chemical structures of coumarin photocages . . . 32

4.4 ICT- and TICT-state of dialkylamino-substituted coumarins . . . 33

4.5 Uncaging mechanism . . . 34

4.6 Molecular structure of the novel photocage system . . . 35

4.7 The synthesis of the triad consisting of antenna, cage and biomolecule . 36 4.8 Proposed photoreaction of the triad . . . 37

4.9 Woodward-Hoffmann-rules explained at the example of 1,6-dimethyl- 1,3,5-hexatriene . . . 38

4.10 Molecular structure of the BODIPY-DTE . . . 39

4.11 Photochromic reactions of fulgides . . . 40

4.12 Molecular structure of the water-soluble indolylfulgimide . . . 41

5.1 Schematic representation of the Spitfire Ace laser system . . . 51

5.2 Schematic representation of the stretcher used for CPA . . . 52

5.3 Schematic representation of the amplifier . . . 54

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5.4 Schematic representation of the compressor . . . 54

5.5 Schematic representation of the pump-probe setup used in this work . . 58

5.6 Chopping scheme used in the ATAS setup . . . 59

5.7 Schematic representation of the most common signals detected in transient absorption spectroscopy . . . 60

5.8 Schematic representation of the TPEF setup . . . 61

5.9 Schematic representation of the Kerr shutter . . . 63

5.10 Mercury lamp spectrum detected with grating 2 . . . 65

5.11 Correction curve for the detector sensitivity . . . 66

6.1 Proposed uncaging reaction of DEACM-Glu . . . 70

6.2 Stationary absorption and fluorescence spectra of DEACM-Glu and of the corresponding photoproduct DEACM-OH in DMSO . . . 70

6.3 UV/vis absorption of DEACM-Glu and DEACM-OH in DMSO and PBS- buffer . . . 71

6.4 Fluorescence bands of DEACM-Glu and DEACM-OH . . . 71

6.5 Absorption spectra of DEACM-Glu in PBS-buffer (0 min-3 min) recorded during continuous illumination (λ= 385 nm) . . . 72

6.6 Continuous illumination of DEACM-Glu in PBS-buffer(1 h-5 h) . . . 73

6.7 Absorption spectra of DEACM-Glu in DMSO recorded during continuous illumination . . . 73

6.8 Transient absorption spectrum of DEACM-Glu in DMSO . . . 75

6.9 Transient absorption spectrum of DEACM-Glu in a solvent mixture . . 76

6.10 Transient absorbance changes of DEACM-Glu at two selected probe wavelengths . . . 77

6.11 Chemical structure of ATTO 390 . . . 77

6.12 UV/vis absorption and fluorescence spectra of ATTO 390 . . . 78

6.13 Transient absorption spectrum of ATTO 390 in DMSO . . . 79

6.14 UV/vis absorption spectra of the triad and the isolated parts . . . 80

6.15 UV/vis absorption and fluorescence spectra of I+II and I+II+III . . . . 81

6.16 Power-dependent two-photon excited fluorescence spectra of rhodamine B and the dyad . . . 82

6.17 UV/vis absorption, two-photon excited fluorescence and two-photon absorption spectra of rhodamine B . . . 83

6.18 a) UV/vis absorption, two-photon excited fluorescence and two-photon absorption spectra of a) fluorescein and of b) coumarin 307 . . . 84

6.19 Two-photon absorption spectra of ATTO 390, I+II and DEACM-OH . . 85

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6.20 Transient absorption spectra of I+II in DMSO at various excitation wavelengths . . . 86 6.21 Ball-and-stick model of two different conformations of the dyad . . . 89 6.22 Formation of the CO2-signal at2337 cm⁻¹during continuous illumination

of caged glutamate . . . 91 6.23 Transient absorbance changes of the triad and of the reference photocage

monitored via FTIR . . . 92 6.24 Wavelength-dependent evolution of CO2 referenced to the absorption

spectrum of the triad . . . 93 6.25 Absorption of I+II+III under continuous illumination at 365 nm moni-

tored in the UV/vis . . . 94 6.26 Absorption of II+III under continuous illumination at365 nmmonitored

in the UV/vis . . . 95 7.1 Stationary absorption and fluorescence spectra of the BODIPY-DTE . . 100 7.2 Transient absorption spectra of the open and the pss of the BODIPY-

DTE dyad . . . 101 7.3 Time-resolved fluorescence of the BODIPY-DTE dyad in the open and

thepss measured with the TCSPC method . . . 102 7.4 Comparison of time-resolved fluorescence and absorption traces of the

pss of the BODIPY-DTE . . . 103 7.5 Stationary absorption and fluorescence spectra of the Z-isomer of the

water-soluble fulgimide . . . 104 7.6 Transient absorption spectrum of the water-soluble fulgimide . . . 105 7.7 Time-resolved fluorescence spectrum of the ring-closing reaction of the

fulgimide . . . 106 7.8 Fluorescence trace at552 nmof the Z-isomer recorded after photoexcita-

tion at 388 nm . . . 107 7.9 Stationary absorption and fluorescence spectra of free FMN and incor-

porated intoMtDod . . . 109 7.10 Transient absorption spectra of FMN andMtDod:FMN . . . 110 7.11 Time-resolved fluorescence trace ofMtDod:FMN . . . 111

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List of Tables

3.1 Comparison of Time-resolved Fluorescence Methods . . . 22

4.1 Photochemical Characteristics of the Four Groups of Coumarin Photocages 32 5.1 Purchased Chemicals Used in this Work and Their Supplier . . . 46

5.2 Composition of the Buffer Solutions . . . 46

5.3 Peak Wavelengths and Bandwidths of LEDs . . . 49

5.4 Lasers Used in this Work . . . 55

6.1 Peak Wavelengths and Referring Power of LEDs Used for IR-uncaging Experiments . . . 93

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List of Abbreviations

1PA one-photon absorption 2PA two-photon absorption

ATAS advanced transientabsorptionspectrometer ACM (7-acetoxycoumarin-4-yl)-methyl

BBO β-bariumborate

BhC (6-bromo-7-hydroxycoumarin-4-yl)methyl) BWD band widthdetector

CaF₂ calcium fluoride

cAMP 3’,5’-cyclic adenosinemonophosphate CCD charge-coupleddevice

CO₂ carbon dioxide

CoA coenzyme A

CPA chirpedpulseamplification CS₂ carbon disulfide

cw continuouswave

DAS decay associatedspectra DCM dichloromethane

DEACM (7-diethylaminocoumarin-4-yl)methyl DMSO dimethylsulfoxide

DMCM (6,7-dimethoxycoumarin-4-yl)methyl)

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Dod dodecin

DTE dithienylethene ET electrontransfer

ESA excitedstate absorption EWG electron-withdrawing group FAD flavin adenine dinucleotide FI Faradayisolator

FLUPS fluorescence upconversionspectroscopy FMN flavin mononucleotide

FRET Försterresonance energy transfer FTIR Fourier-transforminfrared FWHM full width athalf-maximum

g gerade

GLA globallifetimeanalysis GSB groundstatebleach

Glu glutamate

GM Göppert-Mayer

GVD groupvelocitydispersion Hh Halorhodospira halophila

HOMO highest occupied molecular orbital HRR horizontal retroreflector

Hs Halobacteriumsalinarum

HWHM half-width athalf-maximum IC internal conversion

ICT intramolecular chargetransfer

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IET intramolecularenergy transfer IRF instrumentresponsefunction ISC intersystemcrossing

KDP potassium (german: Kalium) dihydrogenphosphate, KH2PO4

LCAO linear combination of atomicorbitals LED light-emitting diode

LUMO lowestunoccupiedmolecularorbital MCM (7-methoxycoumarin-4-yl)methyl MeOH methanol

Mt Mycobaterium tuberculosis

Nd:YVO₄ neodymium-doped yttrium vanadate

Nd:YAG neodymium-doped yttrium-aluminum-garnet Nd:YLF neodymium-doped yttrium lithium fluoride NIR near-infrared

NLT non-linear transmission NMP nucleoside monophosphate

NOPA non-collinear opticalparametricamplifier oNB ortho-nitrobenzyl

OPA opticalparametricamplifier PBS phosphate buffered saline PC Pockelscell

pcFRET photochromicFörsterresonance energy transfer PDA photodiode array

PCM (7-propionyloxycoumarin-4-yl)methyl PMT photomultiplier tube

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PPG photolabileprotecting group

PPLN periodically poledlithium niobate, LiNbO3

PS periscope

pss photostationary state PTFE polytetrafluorethylene Rf riboflavin

SE stimulated emission SFG sumfrequency generation SHG second harmonicgeneration

TCSPC time-correlated single photoncounting TDG time delay generator

TICT twisted intramolecular chargetransfer Ti:Sa titanium-dopedsapphire

TPEF two-photonexcited fluorescence TPIF two-photoninducedfluorescence

u ungerade

VRR vertical retroreflector

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1 Introduction

The indefatigable endeavor for the understanding of processes on a molecular level requires for their observation not only sophisticated techniques but their steady improve- ment. A famous example was the prediction of the simultaneous absorption of two photons in one quantum event, the so called two-photon absorption (2PA), by Maria Göppert-Mayer back in the year 1931.¹ As this process requires high photon density, its experimental evidence was first provided with the invention of the laser by Kaiser and Garrett 30 years later, as they observed fluorescence of Eu²⁺ upon 2PA.² With the proliferation of pulsed high-power lasers, the phenomenon attracted considerable attention due to its outstanding properties such as deeper sample penetration and high three-dimensional resolution accompanied with less phototoxicity, rendering the superi- ority of 2PA in many respects to the common one-photon absorption (1PA).³In analogy to Raman and infrared spectroscopy, 2PA is complementary to 1PA, enabling a ’new’

spectroscopy with favorable characteristics.^4,5 Therefore, the two-photon technique is extensively applied in thriving research fields encountering material science, including data storage, in which different layers of a substance can be addressed to store and retrieve information,^6–11 and microfabrication.^11–19 In addition, 2PA found also application in other fields such as microscopy,^20–28photodynamic therapy^29–35and uncaging reactions where an effector molecule is encapsulated by a photocage and can be released upon irradiation.^36–40Especially the last example joints the technique of 2PA with the strive for highly resolved spatiotemporal control of biological processes with light as harmless and ecological trigger.

At present, the research field exhibits only few potent two-photon activatable photocages as the computational calculation and deliberate design for increased efficiency regarding 2PA is yet an intricate challenge. One part of this work is dedicated to respond to this challenge with a molecular design strategy intended to achieve an enhanced 2PA

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1 Introduction

of a widely used and well-known photocage by introducing a molecular antenna for 2PA sensitization. This approach is based on the fact that readily available fluorophores display a high two-photon response which is by now not reached for photocages. The spectroscopic characterization of the antenna-photocage-system is one of the major ob- jectives in this work, including its ultrafast photodynamics as well as the assessment of its 2PA with regard to the influence of the antenna and its functionality by means of the liberation of a caged molecule upon illumination.

A second class of photoactivatable compounds are photochromic molecules, also known as photoswitches as they are distinguished by the reversible switching upon light activation between at least two isomers. Among the plethora of photochromic compounds, the most prominent are stilbenes and azobenzenes which undergo a pho- toinduced cis-trans isomerization.^41–44 Additionally, photochromic reactions can also be rendered by an electrocyclization in which new bonds are formed or broken as it is found for fulgides (fulgimides) and dithienylethenes which are studied in this work.

Moreover, photoswitches can be jointed with a strong fluorophore, enabling to modu- late the fluorescence due to the photochromism. Aspects of the fluorescence modulation of such a cooperative dyad incorporating a dithienylethene are deduced from complementary time-resolved spectroscopic experiments in this study. Similar systems have already been thoroughly exploited in optical memory devices,^45–48in fluorescent molecular switches^49,50 and as fluorescent markers in biological applications.^51–54Especially, the last example constitutes the necessity of hydrolytic-stable photochromic compounds in aqueous environments. The second photochromic compound investigated in this work, a water-soluble fulgimide, meets this demand as by now only a few photoswitches have been studied in aqueous solution.^55–60 The ultrafast cyclization reaction of this photoresponsive system is spectroscopically characterized in this work.

The fourth photoresponsive system examined in this work is the flavoprotein dodecin. The cofactor flavin is distinguished by its chemical versatility accounted to its redox-active and light-sensory subunit isoalloxazine suiting the flavoprotein for electron transfer reactions e.g. in the citric acid cycle⁶¹or in the flavin-binding DNA photolyase which repairs damaged UV-irradiated DNA.⁶² Dodecins exhibit a quaternary hollow- spheric structure in which the cofactor flavin is incorporated in an unique binding mode facilitating an ultrafast deactivation of the excited state of the flavin.^63–65 In general, dodecins can be divided into archaeal and bacterial flavoproteins where the first is already well characterized. Due to differing structural properties found in these two classes, different functional tasks are deduced. The aim of this work was to understand the function of the bacterial dodecin from Mycobaterium tuberculosis (Mt).

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Part I of this work encompasses the theoretical framework of 2PA, fluorescence and photoactivatable compounds. Particularly, 2PA will be addressed in which a detailed theoretical description will be given (Chapter 2). Moreover, the classification of 2PA via several techniques will be discussed, as the quantitative characterization comprises technical obstacles yielding in partly divergent values for the 2PA. This is often caused by an inaccurate determination of the photon flux which is prone to any uncertainties within the excitation pulse. A solution to overcome this issue is the two-photon excited fluorescence (TPEF) technique.^66,67 In addition, fluorescence as a deactivation process and instrumental techniques to record time-resolved fluorescence are indited (Chapter 3). The last chapter of the theoretical framework (Chapter 4) introduces the molecule classes of photochromic and caged compounds. Part II delineates the materials and the applied experimental methods. Part III is devoted to the results in which Chapter 6 will focus on the spectroscopic characterization of the novel antenna- photocage-system with presumably improved characteristics regarding 2PA. Chapter 7 deals with the ultrafast photodynamics of photoresponsive systems with the emphasis on time-resolved fluorescence on the subpicosecond time scale. Here, the findings of the two photochromic compounds and the flavin-binding protein dodecin are presented. In the end, the achieved results of this work are concisely collated and a brief outlook is given (Part IV).

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1 Introduction

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Part I

Theoretical Framework

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2 Two-Photon Absorption

Two-photon absorption (2PA) is a third order non-linear optical (χ³) process which can be described as simultaneous absorption of two low-energy photons in a quantum event, where the transition energy equals the sum of the energy of the two photons. In detail, a virtual state is created prior to the off-resonant absorption of the first low-energy photon. This virtual state shall not be understood as anEigenzustand of the molecule but more as the interaction of the electric field of the photon with the molecule. The presence of this virtual state, which lives about 5 fs,⁶⁸ allows the second photon to induce a transition from the imaginary to the final state. Mostly, both photons in the 2PA process have the same energy (one-color) which usually corresponds to light of twice the wavelength required to reach an excited state in 1PA. This process is coined degenerated 2PA. The case where the two photons exhibit different levels of energy is called non-degenerated 2PA. Figure 2.1 encompasses in a simplified Jabłoński diagram the two cases of 2PA and the more common 1PA.

The main difference between 1PA and 2PA is the dependence on the photon flux (light intensity). While the involvement of only one photon in 1PA entails a linear dependence on the light intensity, the probability of 2PA exhibits a quadratic dependence, by virtue of the absorption of two photons at the same time. Consequently, the absorption of two photons at the same time can only be observed in focused beams of pulsed lasers with high-power outputs.

The compliant photon density within the use of such lasers and an appropriate lens is highest at the focal point and decreases along the z-axis with the squared distance leading to a very small fraction of excited molecules within the focus (Figure 2.2).

The diffraction limit confines the dimensions of the excited volume approximately to the used excitation wavelength, resulting in a high three-dimensional (3D) resolution for

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2 Two-Photon Absorption E ^|f

›

1PA degenerated

2PA non-degenerated 2PA

|g

›

Figure 2.1: Simplified energy level diagram of one- (left) and two-photon absorption. The degenerated case where two-photons exhibit the same energy is shown in the middle, while the non-degenerated case encloses a transition of two photons with different amount of energies (right).

the process of 2PA. The off-resonant excitation provides the advantage of deeper sample penetration, while the excitation beam in 1PA is directly absorbed as it is incident on the material and further attenuated as it travels through the sample.

1PA P ∝ I 2PA P ∝ I²

molecules in the ground state molecules in the excited state

Figure 2.2: Schematic representation of the main difference between 1PA and 2PA. Within 2PA the quadratic intensity dependence provides 3D-resolution. Furthermore, this process is only observed at focal points with a pertinent photon density accessible with high-power pulsed lasers.⁶⁹

Besides the high 3D-resolution and the deeper sample penetration, 2PA based on IR-light provides the access to the "phototherapeutic window" (690 -950 nm) by means of harmless IR-light.^70,71 The combination of less phototoxicity and the above mentioned advantages enables the application of the 2PA technique to many biological systems.^72–80

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2.1 Theoretical Description of Two-Photon Absorption

According to the Lambert-Beers law, the extinction coefficientεquantifies the strength of the 1PA of a material (Eq. 2.1).⁸¹

A=ε·c·d (2.1)

whereAis the absorbance,c the concentration of the investigated compound andd the optical path length of the sample.

In equivalence to the extinction coefficient, it is possible to express the 2P-response of a material through the so called two-photon cross sectionσ2Pin terms of the propagation equation with given wavelength incident on the 2P absorbing compound (Eq. 2.2).⁸²

dφ

dz =−σ_2P ·N ·φ² (2.2)

Withφ as the the photon flux, N as the number of molecules in the ground state per volume unit and z as the propagation direction of the beam. The determination ofσ2P

of two-photon absorbing materials is very desirable and will be discussed in detail in Section 2.4. At this point, it shall be noted that the σ2P also known as two-photon absorption cross section (or 2PA cross section) is frequently abbreviated by a δ or σ⁽²⁾. The unit of σ_2P is given by m⁴s/(molecule photon). Because of the relatively unwieldy expression the unit Göppert-Mayer (GM), in honor to Maria Göppert-Mayer, is commonly used and is defined as follows: 1 GM = 10⁻⁵⁰ cm⁴s/(molecule photon).

In case of additional 1PA, a second term has to be considered in which Eq. 2.2 becomes Eq. 2.3:⁸²

dφ

dz =−σ_2P ·N ·φ²−ε·N ·φ (2.3) On the basis of the relation of the photon flux φ to the intensity of the beam by the photon energy Eph = ^hc_λ = hν (where h is Planck’s constant and c the speed of light)^3,81,82

φ= I

E_ph (2.4)

Eq. 2.3 can be expressed in terms of the beam intensity:³ dI

dz =−σ_2P Eph

·N·I²−ε·N·I (2.5)

With the considerations made above, a given 2PA band with a Lorentzian line shape resulting from a transition from the ground state |gi to a final state |fi σ_2P can be expressed in Eq. 2.6:³

σ2P = 2π E_ph² L⁴

ε²₀ρ²c²Γ Sf g (2.6)

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2 Two-Photon Absorption

withρ as refractive index, ε0 as the vacuum permittivity, Γ as the half-width at half- maximum (HWHM) and the factor L (L=(n² + 2)/3) which arises from the difference of the optical field in a medium to that in vacuum.

Sfg describes the squared sum of the product of oscillating dipole moment vectors induced by light, which matches the energy difference between the ground and an intermediate state (µ_gi), as well as the energy difference between the intermediate and the final state (µif) divided by the energy difference between the ground and the intermediate state and the energy of one photon involved in the 2PA process. Since the molecule rotates with many dipole moment vectors in solution, an average in the direction of the beam propagation is necessary. An approximated expression of Sfg valid for the most two-photon absorbers is given in Eq. 2.7:³

S_{f g} = 1 5





∆µ_gfµ_gf h ν

2

+ X

i6=f,g

µ²_giµ²_if (Egi−h ν)²

!

 (2.7)

with∆µgf as the difference of the static dipole moment between ground and final state.

The first summand in Eq. 2.7 is called the dipolar term abbreviated with D. The second term is coined the two-photon term (T).

2.2 Selection Rules

Depending on the molecule symmetry different selection rules have to be applied con- cerning 2PA. Considering centrosymmetric molecules all static dipole moments are negligible resulting in an absent dipolar term. The expression ofσ_2Pcan than be simplified to:

σ_2P =C µ²_giµ²_if

(Egi/hν)−1)²Γ (2.8)

whereC is a constant.

For the study of two-photon absorption four states have to be considered. In the present scenario, the ground |gi and the final state |fi which shall have gerade (g) parity, as well as the ungerade (u) intermediate|ii state and a virtual state which are depicted in Figure 2.3.

For centrosymmetric molecules transitions between two states of different parity (g→u and u→g) are electric-dipole-allowed for 1PA. Thus, in this case 1P-transitions are allowed from the ground to the intermediate state (|g_gi → |i_ui) and from the intermediate to the final state (|i_ui → |f_gi), while a direct transition from the ground to the final state is forbidden (|g_gi → |f_gi. In case of 2PA, the photon energy is off-resonant with both transitions |g_gi → |i_ui and |i_ui → |f_gi. However, a virtual state is created, as

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2.3 Enhancement of Two-Photon Cross Sections

E

hν

hν hν

hν

∆ f

|

›

virtual state f

|

›

g

|^g

›

|

›

g

|

›

|i

›

E_gi

Figure 2.3: The four essential states for 2PA shown in the energy level diagram for centrosymmetric (left) and non-centrosymmetric molecules (right).³

the first absorbed low-energy photon interacts with the molecule. Due to its presence and its ungerade parity, the second photon can be absorbed to the final state and is therefore 2PA-allowed.

As a molecule exhibits a dipolar character when it is non-centrosymmetric, the D- term of σ_2P has now to be considered. The |g_gi → |f_ui-transition is then allowed for 1PA and 2PA (|f_uiis nowungerade). However, the T-term (two-photon term) becomes now smaller than the D-term, since the|ii now lies energetically above|f_ui (∆>hν).

The D-term becomes smaller when|iilies below |fi, since∆is now smaller than the photon energy, as seen for centrosymmetric molecules.

In a nutshell, transitions between states bearing the same parity (gerade to gerade orungerade to ungerade) are 2PA-allowed for molecules with an inversion center, while a transition between two states of different parity is 1PA-allowed. An exclusiveness of states which can be reached via 1PA or 2PA does not exist for non-centrosymmetric molecules. However, there is no correlation between 1PA and 2PA transition strengths.

2.3 Enhancement of Two-Photon Cross Sections

The design of efficient 2P absorbers has been, to a certain extent, a trial and error process, since µ²_if- values are experimentally not readily accessible. In contrast, µ²_gi and µ²_gf are proportional to the 1PA oscillator strengths so that their magnitudes can

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be inferred from theoretical calculations. The first attempt to increase the σ2P is the extension of theπ-system within a given molecule as reported by Albotaet al.⁸³and is shown in Figure 2.4.

0 GM 0.9 GM

(530 nm) 12 GM

(514 nm)

~

Figure 2.4: The introduction of extended π-systems within a molecule enhances the σ2P. While theσ2P of benzene is negligible, naphthalene exhibits a measurable value. The stilbene molecule enclosing a conjugated system between two benzenes provides a reasonably highσ_2P.⁶⁹

Another strategy is the introduction of electron-withdrawing (A) and electron-donating (D) substituents to the chromophore which creates a push-pull-system with dipole character enhancing µ²_gf. Those dipolar systems (D-π-A) display a dramatic increase of 2P response as larger charge displacements are present in a transition from a donor-centered HOMO to an acceptor-centered LUMO. This approach can also be applied to symmet- ric systems (D-π-A-π-D and A-π-D-π-A), so called quadrupolar systems.⁸³ A further extent are octupolar systems which expose triangular structures of quadrupolar systems within one molecule (D-(π-A)3 and A-(π-D)3). A σ2P of 450 GM at an excitation wavelength of 740 nm has been reported with this approach.⁶⁹

Since the mentioned approaches to increase σ_2P contain the use of large organic frameworks, an elevated hydrophobicity is caused. In terms of encountering biological demands under physiological conditions, a certain water-solubility should be given claiming a compromise between theσ_2P and the hydrophilic character.

Another approach to enhance the two-photon cross-section is the design of cooperative dyads comprising a strong 2P absorber as an antenna or sensitizer and a photoactivatable compound e. g. a photocage⁸⁴ or a photochromic compound.⁸⁵

2.4 Determination of Two-Photon Cross Sections

To date, a plethora of techniques for the determination of σ2P is available which can be divided into wave-mixing techniques, direct and indirect measurements. All of them are based on different principles exhibiting advantages and disadvantages. Thus, the comparison of absolute σ_2P is very delicate. Rumiet al. reviewed σ_2P-values for N,N- diphenyl-7-[2-(4- pyridinyl)ethenyl]-9,9-di-n-decylfluoren-2-amine (AF-50) and the photochromic bis(dibutylamino)stilbene obtained by different methods revealing substantial

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2.4 Determination of Two-Photon Cross Sections disagreement between published values as they vary several orders of magnitude.⁸² It is therefore difficult to assess a method which provides reliable values for σ_2P. The following sections shall provide a general overview of the two most commonly used experiments to determine σ_2P. While Section 2.4.1 is dedicated to the direct method

’z-scan’, a detailed description will be devoted to the indirect method ’two-photon excited fluorescence’ in Section 2.4.2. The latter was employed in this work to determine σ_2P.

2.4.1 Z-Scan

Direct measurements of σ_2P have great similarity to the characterization of the one- photon absorbance of a compound. Likewise, the attenuation of the 2P excitation beam, as it is absorbed by the sample, is the observed parameter within this method.

The σ_2P can then be derived by detecting the transmittance as the intensity alters.

This is accomplished by varying the spot size with a defined excitation pulse energy or by variation of the excitation pulse energy with given spot size. Z-scan and the non- linear transmission (NLT) method, respectively, avail this strategy. In the latter, the excitation pulse energy is measured before and behind the sample along the propagation plane in a series with different excitation pulse energies. With exact knowledge of the experimental parameters and the pulse properties, the dependence of the transmittance on the excitation energy can be exploited andσ_2P values can be derived.^86–88

sample

lens aperture

wavelength-tunable fs-OPA

z-axis

photodiode

Figure 2.5: Schematic z-scan setup for the determination of σ_2P. The output of the wavelength-tunable OPA is focused with a lens on the sample which is moved along the z- axis. The transmissions at different positions are detected via a photodiode.

In the z-scan experiment the intensity is fixed while the position of the sample along the propagation axis (z-axis) of a focused laser beam is varied. Hence the sample expe- riences different spot sizes and the corresponding transmittance is detected (Figure 2.5).

Since the two-photon process occurs in the focal point, the transmittance should be 1 when the sample is out of the focus range and the off-resonant excitation induces no 1PA. As the sample is translated towards the focal point, the probability of 2PA increases, hence the transmittance decreases and peaks at the maximum intensity, which is at the focal point where z is defined as 0. As the sample is "scanned" further away

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from the focus, the transmittance increases until any two-photon process is absent and the transmittance is 1 again.^88–91By dividingφ² in Eq. 2.2 and integrating over space, σ_2P can be determined using the initial conditionφ(0)for the photon flux at z = 0:⁸²

dφ

φ² =−σ_2P ·N dz Z dφ

φ² =− Z

σ_2P ·N dz

−1 φ+ 1

φ(0) =−σ_2P ·N ·z

(2.9)

By solving Eq. 2.9, the photon flux at each position z is expressed in Eq. 2.10:⁸² φ(z) = φ(0)

1 +σ2P ·N·z·φ(0) (2.10)

In order to diminish the inaccuracy, several measurements of the pulse energy before and behind the sample are performed, although Eq. 2.10 indicates that a single measurement would be sufficient to determine σ_2P. Moreover, the dependence of σ_2P on the difference of two values with similar magnitudes (φ(0)⁻¹ and φ(z)⁻¹, Eq. 2.9) may result in uncertainties requiring a series of measurements. The above mentioned equations apply also to the NLT-experiment with the difference that the sample is fixed and the intensity is varied.

Eq. 2.10 premises an approximately constant beam intensity along the focal plane and that the attenuation of the beam intensity is only occurring from 2PA, neglecting the fact that the intensity differs within a focused beam along the z-axis as considered in Figure 2.5. Taking this into account, further parameters have to be considered in Eq. 2.10. Besides a collimated or a focused beam, the pulse profile which can differ in space and in time has to be deliberated which makes the interpretation of the measurement more sophisticated. The most common combination encompasses a focused beam with a Gaussian profile in space and time and an open aperture. The term "open aperture" is related to the fact that the beam is neither confined by any aperture, nor by the sensor of the detector. The accuracy ofσ2Pgained with this combination within z-scan depends on the deviation of the experimental beam profile to an ideal Gaussian beam which is assumed in the referring equations. However, profiles divergent from the ideal case can lead to systematic errors entailing inaccurate σ_2P.

2.4.2 Two-Photon Excited Fluorescence

Indirect methods monitor deactivation processes of the excited state upon 2PA in order to acquire σ_2P. Two-photon excited fluorescence (TPEF) also known as TPIF (two- photon induced fluorescence) is one of the most prominent experiments belonging to the category of indirect methods.

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2.4 Determination of Two-Photon Cross Sections The process of two-photon induced fluorescence is very similar to the radiative deactivation after one-photon excitation. However, the final state which is reached after two- photon absorption is disregarded as the molecule relaxes non-radiatively within∼1 ps⁹² to the lowest vibrational state of the first electronically excited state (Kasha’s rule).⁹³ From there, the molecule relaxes radiatively or/and non-radiatively to the ground state with a fluorescence lifetime typically in the ns-range. σ2P can be inferred by monitoring the fluorescence intensity. Besides exact knowledge about the spatial and temporal properties of the excitation beam and the characteristics of the experimental setup, in particular of the detection system, it is required to access absoluteσ_2P values. This can be circumvented with the relative measurement in which the intensity of a reference compound with knownσ_2Pis compared to the 2PA response of the investigated sample.

Recently, TPEF studies have been performed in the relative fashion, since the indirect method in an absolute way bears several difficulties. For the purpose of facilitated relative TPEF measurements, Xu and Webb established a reliable database with many reference compounds exhibiting absolute cross section values from the visible to the NIR-range.^66,67

With TPEF a two-photon action cross section (σ_TPA) can be determined which displays a linear dependence on the product of σ2P and the fluorescence quantum yield (φ_fl) upon two-photon activation (Eq. 2.11).^66,67

σ_{T P A}=φ_{f l}σ_2P (2.11)

In the two-photon induced fluorescence process the number of absorbed photons per time unit (N(t)) is twice the number of fluorescence photons per time unit (F(t)).

Under the assumption that self-quenching or stimulated emission effects are absent, the relation between absorbed and emitted photons is directly correlated to the experimental emission collection efficiencyψ and can thus be expressed as in Eq. 2.12.^66,67

F(t) = 1

2ψ φ_{f l}N(t) (2.12)

The measure in this experiment is the time-averaged fluorescence hF(t)i which can be expressed as:^66,67

hF(t)i= 1

2ψ φ_{f l}σ_2Pcgp

f τ

8ρhP(t)i²

π λ (2.13)

withc as the concentration,ρ as the refractive index of the solvent,λas the excitation wavelength,hP(t)i as the time-averaged power and g as parameter of the pulse shape,

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τ as the full width at half-maximum (FWHM) andf as the repetition rate of the laser.

Eq. 2.13 comprises relevant parameters such as the fluorescence collection efficiency or the degree of second-order temporal coherence (gp) which have to be characterized in absolute measurements. Nonetheless, the determination of these parameters can be avoided by using standard calibration samples with known two-photon action cross sections and new σTPA can be derived from the ratio of measured fluorescence signals Eq. 2.14.^66,67

hF(t)i_cal

hF(t)i_new = ψ_cal·φ_{f l,cal}·σ_2P,cal·c_cal· hP_cal(t)i²·η_cal

ψ_new·φ_{f l,new}·σ_2P,new·c_new· hP_new(t)i²·η_new (2.14) withcal as index for the calibration sample and new as index for the compound with the to determinable σTPA. Under identical conditions the ratio of fluorescence signals can be simplified to:^66,67

φ_f,newσ_2P,new= hF(t)i_new hF(t)i_cal

c_cal c_new

η_cal

η_newφ_f,calσ_2P,cal (2.15) Theσ_TPA can now be calculated with knowledge about concentration, refractive index, incident pulse power, theσ_TPA of the calibration sample and the measured fluorescence intensities.

The schematic setup is depicted in Figure 5.8 in Section 5.5.2 where the pulse of a wavelength-tunable laser is continuously monitored with a fiber spectrometer to diminish any uncertainties of the pulse within the measurements. The beam is focused with a microscope objective on the sample. The generated fluorescence upon two-photon absorption is subsequently collected with a second objective and guided to the detector, while any scattering or back reflections can be depleted with adequate filters.

In order to obtain a broadband two-photon absorption spectrum withσ_TPA, the sample can be excited with 2P with various wavelengths. Before a wavelength-dependent measurement is performed, a power-dependent experiment should be carried out by varying the pulse intensity at a fixed excitation wavelength. This procedure displays whether the dependence of the fluorescence intensity on the squared laser beam intensity is given. Otherwise the results could be misinterpreted. Stimulated emission, ground state depletion, linear absorption and excited state absorption may be reasons for de- viations from the dependence on the quadratic laser intensity. Moreover, a broadband fluorescence detection is advantageous, as scattered light, cosmic peaks or other arti- facts would lead to an overestimation of detected light for example by using a photon counter.

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2.4 Determination of Two-Photon Cross Sections Fluorescence as measure for two-photon excitation is advantageous since it is very sensitive. Thus high energy pulses are not required as in the case of z-scan. However, the pronounced dependence on the spontaneous emission confines the method to molecules with a fluorescent character. Apart of the pertinent fluorescence, the method requires detailed knowledge of the fluorescence properties, particularly the fluorescence quantum yield upon 2PA. Since this parameter is hard to determine, the approximation of 1P fluorescence quantum yields have to be made. Hence, strong fluorescent signals do not indicate directly largeσ2P as the fluorescence quantum yield has to be considered.

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3 Fluorescence

This chapter provides a general overview to fluorescence. Section 3.1 gives insight into the basic principles of fluorescence, while Section 3.2 will focus more closely on the spectroscopic instrumentation for capturing fluorescence. In particular the Kerr shutter as time-resolved method for the observation of fluorescence will be discussed.

In the past decades the attention on fluorescence as non-invasive technology to investigate matter increased significantly. Nowadays, fluorescence has become an indispensable method, based on its high sensitivity and the ease of applicability in biological issues and demands.^92,94,95 It is considered as one of the leading tools in the research field of biochemistry, biophysics and physical chemistry but has also a substantial impact in other disciplines as depicted in Figure 3.1.

BIOCHEMISTRY – MOLECULAR BIOLOGY

64,880

PHYSICAL CHEMISTRY

57,993

MULTIDISCIPLINARY CHEMISTRY

50,780

ANALYTICAL CHEMISTRY

47,049

OPTICS

34,118

MULTIDISCIPLINARY MATERIAL SCIENCES

33,978

BIOPHYSICS

28,921

BIOCHEMICAL RESEARCH METHODS

27,561

APPLIED PHYSICS

24,782

ATOMIC, MOLECULAR &

CHEMICAL PHYSICS

24,612

Figure 3.1: Fluorescence-related publications in different research fields visualize the massive impact of fluorescence as indispensable tool for non-invasive investigation of matter.⁹⁶

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3 Fluorescence

3.1 Basic Principles on Fluorescence Spectroscopy

Interaction of electromagnetic radiation with matter can lead to the absorption of a photon when its energy matches the transition energy between an occupied and an un- occupied state.^81,92From the excited state various processes can take place (Figure 3.2).

Radiation-free deactivation is achieved by converting the electronic energy into rota- tional, translational and vibrational energy. On the other hand, radiative relaxation from an excited state back to the ground state is called luminescence, in particular fluorescence and phosphorescence. The type of luminescence is defined by the multiplicity of the excited state from where it is emitted. Fluorescence is the spontaneous emission of a photon from an excited singlet state.

E

S₀ S₁ S₂ S_n

ν₀ ν₁ ν₂ ν₀ ν₁ ν₀ ν₁ ν₀ ν₁

T₁ ν₀ ν₁

phosphorescence internal conversion

vibra�onal relaxa�on

intersystem crossing ﬂuorescence

absorbance

Figure 3.2: Jabłoński diagram with schematic representation of processes occurring between the electronic and the vibrational states after an initial absorption of a photon. The diagram is based on reference 97.

After the initial absorption into an excited vibronic state, the molecule descends to the lowest vibrational level of the reached excited state (vibrational relaxation). From there, the molecule can relax radiation-free to a vibrational level of a lower singlet state which is called internal conversion (IC). The molecule undergoes these two processes until it reaches the lowest vibrational level of the lowest excited state, the S1-state.

These radiationless relaxation pathways are usually very fast. Times for the internal conversion are typically in the order of 10⁻¹²s^92,98which is the reason for the subsequent emission from the first excited state. This is manifested in "Kasha’s rule".⁹³

Exceptions from this rule are observed for example for azulene, 1,4,7-triazacycl[3,3,3]-

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3.1 Basic Principles on Fluorescence Spectroscopy azine and ovalene which violate Kasha’s rule by fluorescing from the S2-state. In particular, certain circumstances are necessary for the violation of Kasha’s rule. In case of azulene with an IC-time of 10⁻¹²s and 1,4,7-triazacycl[3,3,3]azine the energy gap between the S2 and the S1-state is comparatively high, thus the IC related to these two states is much slower than the S1→S0-transition. As a result, a photoexcited azulene⁹⁹ and 1,4,7-triazacycl[3,3,3]-azine^100,101 emit from the S2-state. Another reason leading to an exception of Kasha’s rule can be seen on the example of ovalene, where the energy gap between S2 and S0 is large but the transition gap between S1 and S2 and the oscillator strength of the S0→S1-transition are very low.^102,103 In this case, a relative long fluorescence lifetime from the S1-state and a thermal population of the S2-state are observed and hence the S2→S0-emission becomes competitive to the typical emission from the S1-state. This so called two-level emission can be suppressed at lower tem- peratures as the thermal population of the S2-state decreases. The third exception to this rule was detected for several hydrocarbons with a reasonable high sensitivity, where triplet-triplet annihilation was used in order to diminish any stray light sources.^104,105

As the molecule is in the lowest vibrational level of the lowest excited state (S1), a vertical transition to the electronic ground state (S0) takes place in accordance to the Franck-Condon-principle. Due to the previously dissipated energy by translational, ro- tational or vibrational relaxation, fluorescence is shifted to higher wavelengths in respect to the absorbance which refers to the Stokes shift. A further reason for red-shifted fluorescence is based on solvent reorganization. The transition from the first excited to the ground state (S1→S0), where the two unpaired electrons in the ground and the excited state exhibit opposite spin-orientation, is completed after a few nanoseconds.⁹² Typical spontaneous emission rates are therefore in the range of10⁻⁸s⁻¹ whereas phosphorescence takes place on a time scale of microseconds to hours. In general, phosphorescence occurs when the molecule undergoes intersystem crossing (ISC) which is an isoenergetic transition between two states of different multiplicity. This optically forbidden process from a singlet to a triplet state can only be realized by a strong magnetic field. In case of light, the intrinsic magnetic field is easily compensated by its electric field. Nevertheless, strong spin-orbit-coupling, an intrinsic perturbation of the molecule, can cause a spin flip of the excited electron. As a result the spins in the ground and in the electronically excited state display the same orientation. From there, the molecule descends the vibrational states until it is trapped at the lowest triplet energy level T1, since a return to the ground state is again spin-forbidden. However, a strong spin-orbit-coupling relaxes the spin forbidden transition by a further spin flip. Consequently, long-lived emission by means of phosphorescence is detected as a result of the recombined electrons in the ground state.

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3 Fluorescence

3.2 Time-Resolved Fluorescence

Time-correlated single photon counting (TCSPC) is characterized by its ease of use and therefore considered as the most-widely applied technique to investigate fluorescence behavior in the ns-range.^106–108 The method TCSPC comprises a relatively inexpen- sive setup which is distinguished by high sensitivity. The principle is based on the assumption that the probability of a single photon detected at a certain time delay is proportional to the fluorescence intensity at this very time. Hence, many excitation pulses cause a fluorescence decay histogram from which a lifetime of the excited state can be inferred.

In practical, the excitation pulse is split, where one part is directly detected by a photodiode setting the starting value and the second fraction is used to photoexcite the sample and thus generate fluorescence. As a photomultiplier, which serves as a photon counter, detects one incoming fluorescence photon, the stop-signal is set. This start- stop-sequence is repeated over several times and yields the above mentioned histogram.

Besides the above mentioned advantages, the highest-achieved time-resolution of the TCSPC is in the range of some picoseconds convoluted by the instrumental response.¹⁰⁹ Observation of fluorescence dynamics in the femto- to picosecond range requires other techniques i.e. the Kerr shutter or the upconversion. Both methods rely on the technique of optical gating.^109–111

Table 3.1: Comparison of Time-resolved Fluorescence Methods.¹¹²

method time resolution remarks

TCSPC 20-30 ps electronics-limited IRF

streak camera 2-10 ps ease of use

upconversion 40 fs¹¹³ difficult alignment

Kerr shutter 100 fs¹¹⁴ broadband spectra

While the upconversion provides single-wavelength fluorescence traces by monitoring the sum frequency of a so called gate pulse and the spontaneous emission, broadband fluorescence spectra can be obtained with the Kerr shutter. This method for capturing ultrafast fluorescence depends on the Kerr effect which refers to the birefringence induced in an optical material upon application of an electric field. This is realized by focusing a ’gate pulse’ and the polarized fluorescence on an isotropic Kerr medium between two polarizers with crossed orientation to each other. Hence, anisotropy is generated and subsequently, a change in polarization of the fluorescence is induced,

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3.2 Time-Resolved Fluorescence allowing a certain amount to pass through the second polarizer.

3.2.1 Optical Gating

The Kerr shutter and the upconversion rely on the principle of optical gating where fluorescence light and a gate pulse are superimposed in an optical switch. Thus, the gate pulse induces temporary modifications of the fluorescence characteristics and hence a time-resolution, which depends in first approximation on the length of the used laser pulses, is created.

delay

op�cal switch stage

gated light ﬂuorescence

gate pulse

Figure 3.3: Schematic representation of optical gating as it is realized for the upconversion and for the Kerr shutter.

By varying the path length of the gate pulse with respect to the excitation pulse, a time delay between the two pulses is introduced in order to monitor fluorescence spectra time-dependently. Each variation of the beam path∆s results in a change of time∆t in respect to the speed of lightc (Eq. 3.1).⁸¹

∆t= ∆s

c (3.1)

The optical switch used in the upconversion is a β-barium borate crystal (β-BaB2O4) abbreviated as BBO which is applied in many non-linear optical processes, due to its large birefringence and small dispersion.¹¹⁵ Generated fluorescence light with the frequencyω_fland the wave vector~k_flis focused together with the gate pulse (ω_g,~k_g) into the BBO-crystal. In the case of temporal and spatial overlap of both pulses, frequency mixing takes place due to the non-linear2^ndorder susceptibility (χ⁽²⁾) at perfect phase matching conditions (Eq. 3.2):¹¹⁶

∆~k= ∆~k_{f l}+ ∆~k_g−∆~k_s= 0 (3.2) and a sum frequency signal is obtained:¹¹⁶

ωs=ω_{f l}+ωg (3.3)

In this non-linear process energy and momentum are conserved, leading to no dissipa- tive energy. A drawback of this technique is the fact that the thickness of the crystal

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3 Fluorescence

and fixed crystal angles restrict the phase matching only to a small frequency range.

Therefore, obtaining transient fluorescence spectra via the upconversion method is ag- gravated. One approach to realize a broadband fluorescence spectrum would be the use of many scans, each with varying phase matching angles. This technique demands long measurement times and entails the drawback of obtaining low quality spectra caused by low-frequency noise. Another approach to enlarge the acceptance band width ∆ν can be inferred by Eq. 3.4.¹¹⁷

∆ν∼

1 d

c

V(νs) −_V_(ν^c

f l)

(3.4)

with V as the group velocities of the light and d as the thickness of the non-linear crystal. Hence, a thin crystal with low-dispersion such as KDP (potassium dihydro- gen phosphate, KH2PO4) should positively affect ∆ν. Furthermore, gate pulses in the infrared region should decrease the dispersion. Thus it is possible to obtain a broad spectral range of 10.000 cm⁻¹ by using a KDP-crystal with a thickness of (0.1 mm) and a gate pulse with a central wavelength of 1300 nm.¹¹⁸ This method with the acronym FLUPS (fluorescence upconversion spectroscopy) became very popular in terms of ultrafast spectroscopy and is nowadays commercially available.

Differently, phase matching conditions have not to been considered with the Kerr shutter used in this work. It therefore provides intrinsically broadband fluorescence spectra. On the other hand, the time resolution becomes worse compared to the IRF (instrument response function) of the upconversion which is in the range of couple of ten femtoseconds. Nevertheless, time resolution below 100 fscan be achieved with the Kerr shutter.

3.2.2 Kerr Shutter

The Principle

In contrast to linear optics, the linear proportionality between the polarizationP~ and the electric field strengthE~ is not given in non-linear optics anymore, due to the interaction of high-energetic laser light with electrons. While the first term of Eq. 3.5 would suffice to describe a linear relationship between P~ and E~, the non-linearity, found in the processes exploited by the upconversion or the Kerr shutter, can be represented by a Taylor series development of polarization in higher order terms depending on the electric field strength.¹¹⁹

P(~ E(t)) =~ ε₀h

χ⁽¹⁾·E(t) + (χ~ ⁽²⁾·E(t))~ ·E(t) + (χ~ ⁽³⁾·E(t)~ ·E(t))~ ·E(t) +~ ...i (3.5)

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3.2 Time-Resolved Fluorescence where ε0 is the absolute dielectric constant in vacuum and χ(n) are the n^th order of the dielectric susceptibility tensors which are way smaller for higher orders and can be therefore neglected at small electric field strengths.

While the upconversion is an optical method relying on a non-linear2^ndorder process, the Kerr shutter is based on the non-linear3^rd order susceptibility (χ⁽³⁾) of a material which is proportional to the non-linear part of its refractive index n₀. The Kerr effect, also known as the quadratic electrooptic effect, often uses isotropic media as Kerr medium, hence the 2^nd order susceptibility becomes zero and χ⁽²⁾-processes e.g. sum frequency generation are minimized. The first and the third order of the polarization P~ yields the total polarization of the Kerr medium (Eq. 3.6):

P~(E(t)) =~ P~⁽¹⁾(E(t)) +~ P~⁽³⁾(E(t))~

=ε₀h

χ⁽¹⁾·E(t) +~

χ⁽³⁾·E(t)~ ·E(t)~ ·E(t)~ i

=ε0

h

χ⁽¹⁾+χ⁽³⁾·(E~(t))²

·E(t)~ i

(3.6)

By applying a strong time-dependent electric field, the refractive index n is changed by a non-linear intensity-dependent part which is described with the following equation:^120–122

nI,t=n0+n2I(t) =n0+ ∆n(t) (3.7) withn₀ as the refractive index without the electric field and ∆n as the change of the refractive index in respect to the polarization of the gate pulse. The refractive index is independent of the intensity of the electric fieldI(t), thus the expression is extended by n2 which considers the strength of the applied field to the intensity over time:¹²³

n2 ≈ 1

n²₀ε₀c ·χ⁽³⁾ (3.8)

The intensity is given by:¹²³

I = 1

2 ·n0ε0c|E|² (3.9)

Kerr gating can be realized upon photoexcitation of the investigated sample. The generated fluorescence is collected via a Schwarzschild objective and then passed through a polarizer. The linear polarized fluorescence is impinged on the isotropic Kerr medium which is located between two crossed thin-film polarizers. Due to the crossed orientation of the analyzer (second polarizer) with respect to the first polarizer, the linear polarized fluorescence is not able to pass through the analyzer. In presence of the gate pulse and temporal and spatial overlap with the fluorescence light, birefringence is induced, hence anisotropy leads to partly change of the polarization of the fluorescence impulse which is not anymore linear but elliptical.¹²⁴ A certain amount is now able to pass through the gate for detection which is open for the duration of the length of the gate pulse.

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3 Fluorescence

Since this principle is only based on the anisotropic change of the refractive index and is therefore wavelength-independent, the Kerr shutter does not have to meet any phase matching conditions to obtain broadband emission spectra. By varying the length of the beam path of the gate pulse with respect to the excitation pulse via an electronic delay line, the intensity of the fluorescence can be detected at different delay times.

without gate pulse

n₁ n₂

delay stage gate pulse

with n₁ n₂ gate pulse

analyzer Kerr medium

polarizer sample

detector detector

Figure 3.4: Schematic representation of the Kerr shutter principle. In the absence of the gate pulse (upper case) the fluorescence is blocked by the analyzer, while in the lower scenario anisotropy is induced in the Kerr medium by the gate pulse and fluorescence is gated to the detector.

A very important parameter of the Kerr shutter is the gating efficiencyT which is the ratio between gated fluorescence and total fluorescence impinged on the Kerr shutter per time unit. The efficiency depends on the phase shifting φ(t) and on the angle Ω between the two polarization faces of fluorescence and gate pulse. The phase shifting can be expressed in the following way:^124,125

φ(t) =

2πδn(t)l λf l

(3.10) while the gating efficiency can be described as in Eq. 3.11:^125,126

T ∼sin²(2Ω)·sin² 1

2φ(t)

(3.11) On the basis of Eq. 3.11 the gating efficiency reaches its maximum at an angle of 45^◦ forΩ. Under the assumption of very lowφ(t)the gating efficiency can be approximated by Eq. 3.12:

T ≈

πn2lI λ_{f l}

2

(3.12)

Spectroscopic characterization of photoresponsive systems: from chromoproteins to switchable and caged compounds